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The Journal of Experimental Biology 201, 63–70 (1998) 63 Printed in Great Britain © The Company of Biologists Limited 1998 JEB1084

STRESSES IN HUMAN MUSCLES IN RUNNING AND JUMPING DETERMINED BY FORCE PLATE ANALYSIS AND FROM PUBLISHED MAGNETIC RESONANCE IMAGES

SUSANNAH K. S. THORPE1,*, YU LI1, ROBIN H. CROMPTON1 AND R. MCNEILL ALEXANDER2 1Department of Human and Cell Biology, Liverpool University, New Medical School, Ashton Street, Liverpool L69 3GE, UK and 2Department of Biology, Leeds University, Leeds LS2 9JT, UK *e-mail: [email protected]

Accepted 6 October 1997; published on WWW 9 December 1997

Summary Calculation of the stresses exerted by human muscles to 150 kN m−2 during running at 4 m s−1. In the quadriceps, requires knowledge of their physiological cross-sectional peak stresses ranged from 190 kN m−2 during standing long area (PCSA). Magnetic resonance imaging (MRI) has made jumps to 280 kN m−2 during standing high jumps. Similar it possible to measure PCSAs of leg muscles of healthy stresses were calculated from published measurements of human subjects, which are much larger than the PCSAs of moments. These stresses are lower than those cadaveric leg muscles that have been used in previous previously calculated from cadaveric data, but are in the studies. We have used published MRI data, together with range expected from physiological experiments on isolated our own force-plate records and films of running and muscles. jumping humans, to calculate stresses in the major groups of leg muscles. Peak stresses in the surae ranged Key words: muscle stress, magnetic resonance imaging, force-plate from 100 kN m−2 during take off for standing high jumps records, human, muscle, physiological cross-sectional area.

Introduction Physiological experiments on isolated muscles or fibre However, their analysis was confined to the muscles and bundles have provided information about the stresses that to isometric contraction. mammalian muscles can exert, both in isometric conditions MRI is considered to be the most accurate and detailed and when lengthening or shortening (Close, 1972). However, imaging technique currently in use (Beneke et al. 1991; very little is known about the stresses that act in human Engstrom et al. 1991; Scott et al. 1993). Its high resolution muscles during everyday activities, and what little information gives clear distinction between fat, muscle, connective tissue we have is open to criticism. Alexander and Vernon (1975) and . The use of MRI to measure physiological cross- combined the muscle dimensions of cadaver with the sectional areas of muscles from healthy subjects in vivo also forces exerted during various activities by live subjects in order eliminates the problems of cadaveric data. Thus, the aim of the to calculate the stresses involved. However, physiological present study was to calculate accurate muscle stresses by cross-sectional areas of muscles taken from cadaveric material combining moments of force with these muscle dimensions. are generally much lower than expected for healthy living The moments of force exerted during a range of activities are subjects, as the present paper will show. The use of cadaveric well documented in various studies (Alexander and Vernon, data will generally result in an overestimation of the calculated 1975; Mann, 1981; Winter, 1983; Bobbert and van Ingen stresses (Alexander and Vernon, 1975). Maughan et al. (1983) Schenau, 1988; De Vita, 1994; McCaw and De Vita, 1995); avoided the problems of cadaveric material by using cross- however, only two (Alexander and Vernon, 1975; Bobbert and sectional areas obtained by computer tomography of healthy van Ingen Schenau, 1988) have also presented the angles of subjects but, as the stresses were calculated from anatomical the during the activity, which are required for the rather than physiological cross-sectional area (i.e. without calculation of moment . Consequently, the present study taking account of muscle pennation), they do not help us to will use the moments of force presented in these two papers, relate muscle performance to the results of experiments on and new data for running and jumping, to calculate muscle isolated fibre bundles. Recently, Fukunaga et al. (1996) have stresses. combined muscle dimensions obtained using MRI with ankle joint moments obtained using a dynamometer for various joint angles taken from the same subject. This method obviously Materials and methods eliminates all inaccuracies due to subject differences. Information concerning the subjects is shown in Table 1. 64 S. K. S. THORPE AND OTHERS

Table 1. Subject information Number of Age Height Mass Measurement Reference subjects (years) (m) (kg) Mass/height PCSA: triceps surae Fukunaga et al. (1992) 11M, 1F 32±8.2 1.76±0.06 73.5±9.4 41.8 PCSA: quadriceps Narici et al. (1992) 6M 34±4.7 1.74±0.04 74.1±8.2 42.6 PCSA: Cutts (1988) 1M 27 1.75 73.5 42.0 PCSA: gluteus and Friederich and Brand (1990) 1M Cadaver 37 1.83 91.0 49.7 adductors MA: ankle Rugg et al. (1990) 10M 30±5.9 1.8±0.07 77.5±5.6 43.1 MA: Spoor and van Leeuwen (1992) 1F Cadaver 89 1.56 −− MA: Nemeth and Ohlsen (1985) 10M, 10F 67±6.0 1.71±0.03 68.0±6.0 39.8 MA: hip Visser et al. (1990)* 2M, 3F − 1.57±0.08 −− GRF Present study 2M 25 1.81 75.4 41.7 23 1.79 76.5 42.7 Moments Alexander and Vernon (1975) 2M 37 1.69 68.0 40.2 43 1.68 68.0 40.5 Moments Bobbert and van Ingen Schenau 10M 23±3.0 1.93±0.06 84.0±9.3 43.5 (1988)

Values are means ± S.D. for the number of subjects. M, male; F, female. *Visser et al. (1990) do not provide data on the height and mass of their subjects; however, leg lengths are provided and height was estimated on the basis of the leg being 49.1 % of the height of the subject (Winter, 1990). PCSA, physiological cross-sectional area; MA, moment ; GRF, ground reaction force.

Table 2. Values of physiological cross-sectional area taken from the literature Physiological cross-sectional areas (cm2) Author Method G S RF VL VI VM SM ST BF GM AM AB AL Alexander and Vernon (1975) Cadaver 35 67 30 43 28 34 30 9 26 −−−− Wickiewicz et al. (1983)† Cadaver 29 58 15 28 40 22 19 6.3 16 − 20 3.9 6.0 Friederich and Brand (1990)* Cadaver 65 187 43 64 82 67 46 23 36 60 61 17 23 Cutts (1988)* CT −−78 87 53 70 72 25 69 −−−− Fukunaga et al. (1992)* MRI 96 230 −− − − − − −−−−− Narici et al. (1992)* MRI −−66 62 84 68 −−−−−−−

*Used in present study. †Subject 1. G, gastrocnemius medialis and lateralis; S, soleus; RF, rectus femoris; VL, vastus lateralis; VI, vastus intermedius; VM, ; SM, semimembranosus; ST, semitendinosus; BF, biceps femoris; GM, ; AM, adductor magnus; AB, adductor brevis; AL, adductor longus; CT, computer tomography; MRI, magnetic resonance imaging.

Physiological cross-sectional areas (PCSAs) are given in Table two subjects, matched as closely as possible to those from 2. The PCSAs used in this paper are taken from MRI studies which the MRI data were taken (see Table 1). Both subjects by Narici et al. (1992) for the quadriceps and Fukunaga et al. took regular exercise. Each subject was instructed to run at (1992) for the triceps surae. The subjects used in these studies comfortable and high speeds over a Kistler force platform type are of similar mass and stature. Additional PCSAs are needed 9281B, which was installed in a 10 m long walkway. Standing for the hamstrings, adductors and in order to high jumps and long jumps were also recorded. The subjects calculate the total quadriceps stress. MRI data are not available were allowed to practice over the force plate several times for these muscles, so PCSAs for the hamstrings are taken from before the records were taken to ensure that the running computer tomography (CT) (Cutts, 1988) and for the adductors sequences were natural. They performed each locomotor and gluteus maximus from cadaveric material (Friederich and activity six times to ensure suitable records were obtained. Brand, 1990). The cadaveric values may be rather low and thus Only those trials in which the was fully on the platform result in an overestimation of the stresses in the hip extensors. in a smooth, unbroken stride were selected for analysis. All Force-plate records of running and jumping were made for tests were performed barefoot. muscle stresses 65

Split-frame video recordings (25 frames s−1) were taken of 50 fields s−1 (see Alexander, 1983, on the resolution of all sequences from lateral and anterior viewpoints using Lanczos’ smoothing technique). However, the inertial forces genlocked orthogonal cameras. A time and event marker was and moments were in any case quite small. The mass and connected to the camera to indicate the time at which foot moment of inertia of the shank and were estimated from contact was first made. Each subject had black crosses drawn data in Winter (1990) taking account of the body mass and on the following anatomical landmarks: hip (greater stature of the subjects. ), knee (lateral epicondyle of the ) and ankle (lateral ). The output of the force plate gave the Experimental study: calculation of muscle stresses coordinates of the centre of pressure, which were used to locate Muscle stresses for the hip (h), knee (k) and ankle (a) were the ground reaction force on the video images. Kinetic and calculated assuming that the moment of force of a particular kinematic measurements were analysed at intervals of 0.02 s muscle at a joint was dependent on the PCSA (A), the moment throughout the stance phase of the stride. arm of the muscle about the corresponding joint for any particular joint angle (r) and the muscle stress (σ). It was Experimental study: calculation of moments of force assumed that the triceps surae (TS) exert σa, the quadriceps (Q) Only moments in the sagittal plane were calculated. The exert σk and the adductors, hamstrings (except for the biceps magnitude and direction of the ground reaction force and the femoris longus) and gluteus maximus (AHG) exert σh. (The coordinates of the centre of pressure and of the ankle joint (as adductors are included because they also act as hip flexors and seen in the video image) were used to calculate the moment extensors; Moore, 1985.) The gastrocnemius (GA) and the about the ankle. Moments due to the weight and inertia of the hamstrings (including biceps femoris longus) (H*) also exert foot were ignored as negligible since the acceleration of the moments about the knee, and the rectus femoris (R) exerts a centre of mass of the foot is very small when the foot is on the moment at the hip. Therefore, the moments at the ankle (Ma), ground. knee (Mk) and hip (Mh) are: The free body diagrams shown in Fig. 1 were used to calculate the moments at the knee and hip (see Winter, 1990). TS σ The linear and angular accelerations of the shank and thigh Ma = Α Ara a , (1) were obtained from the video images using a seven-point smoothing technique (Lanczos, 1957). Higher-frequency Q H* GA σ − σ − σ components of these accelerations could not be resolved Mk = Α Ark k Α Ark h Α Ark a , (2) because the framing rate of the video camera was only AHG σ − σ Mh = Α Arh h (Arh)R k . (3)

Axis of hip In these equations, the three muscle stresses are the only unknown quantities. The ankle muscle stress (σa) can be calculated directly from equation 1. Equations 2 and 3 both Centre of mass have two unknowns, σk and σh, and were therefore solved of thigh simultaneously. Axis of knee Axis of knee Moment arms for the triceps surae at the ankle are from Rugg et al. (1990). The effective moment arms of the quadriceps, gastrocnemius and hamstrings at the knee were Centre of mass Centre of mass taken from Spoor and van Leeuwen (1992), using data from of shank of shank their travel experiments. The effective moment arms calculated from tendon travel have the advantage that there is Axis of ankle Axis of ankle no need to take separate account of the geometry of the (Ellis et al. 1980). The moment arms of the hamstrings, adductor magnus and gluteus maximus at the hip are taken from Nemeth and Ohlsen (1985) and of the rectus femoris at Fig. 1. Free body diagrams used to calculate the moments of force at the hip from Visser et al. (1990). Moment arms obtained from the knee and hip. The large arrows at the foot are the components of Spoor and van Leeuwen (1992) and Visser et al. (1990) are the ground reaction force, and those at the knee and hip are the taken from subjects much smaller than those used in the rest components of the resultant force exerted by the thigh on the shank and by the trunk on the thigh, respectively. At the centre of mass of of the analysis (see Table 1). Consequently, these moment the shank/thigh, the straight arrows represent the components of arms were scaled to the height of the experimental subjects. inertial force and the circular arrows represent the inertial moments. Moment arm values for the adductors brevis and longus were The circular arrows at the joints represent the moments exerted about unavailable, so the moment arm of the adductor magnus was these joints by the muscles. taken to be representative of the adductor group. This is a 66 S. K. S. THORPE AND OTHERS

Table 3. Example calculation of the moment and force of the hip extensors

PCSA MA PCSA × MA Contribution to Mh Force 2 3 Muscle (cm ) (cm) (cm ) % of Mh (N m) (N) Adductors 59.77 2.8 167.4 10.6 −11.6 415.4 Hamstrings 166.2 7.6 1263.1 79.7 −87.8 1155.2 Gluteus maximus 20.2 7.6 153.5 9.7 −10.7 140.4 Total 246.2 1584 100.0 −110.1 1711.1

The total moment at the hip (Mh) is known from the kinetic analysis. It is assumed that this moment is made up of contributions from each muscle in proportion to its physiological cross-sectional area (PCSA) multiplied by its moment arm (MA). From this, the force in the hamstrings can be calculated.

Table 4. Example calculation of the moment exerted at the knee by the hamstrings Contribution to moment PCSA % of hamstring hamstring force Moment arm at knee Muscle (cm2) force (N) (cm) (N m) Biceps femoris 69.0 41.6 −480.2 1.8 −8.6 Semimembranosus 72.0 43.4 −501.1 4.3 −21.5 Semitendinosus 25.0 15.1 −174.0 4.3 −7.5 Total 166.0 100.0 −1155.2 −37.6

The force in each of the hamstrings is taken to be in proportion to the physiological cross-sectional area (PCSA) of each muscle. From this, the moment at the knee of each of the hamstrings can be calculated using the total hamstrings force taken from Table 3. reasonable assumption because the muscles have relatively moment was at a maximum, the perpendicular distance from similar lines of action. the resultant force to the axis of the hip joint was measured In order to assess the role of the hamstrings at the knee, we from their Fig. 3 (which gives positions and resultant assumed that the stresses in the gluteus, hamstrings and forces) and multiplied by the ground reaction force. This adductors were equal. This enabled us to calculate the total method does not take account of inertial moments or of the force acting in the hamstrings (Table 3). In Table 4, we moment due to gravity; however, these were small in the estimated the moment of each of the hamstrings about the knee experimental study. In Bobbert and van Ingen Schenau (1988), by calculating the force acting in each muscle on the basis of the joint moments of force and joint angles are provided for its PCSA and multiplying the force by the moment arm of each the take-off phase of a squat jump. Calculations of muscle hamstring at the knee to obtain the moment. This method relies stress were made at 10 % intervals of the stance phase. on the assumption that the distribution of force in groups of For both studies, PCSAs and moment arms were obtained cooperating muscles is proportional to the PCSA. as for the experimental study. Moment arms provided in the Equations 1–3 assume that the triceps surae, quadriceps and literature do not extend to the very bent joint positions hamstrings are active at all times. This seems a valid exhibited in the push-off phase of squat jumps and assumption (for the activities being investigated) for the consequently had to be extrapolated from the curve for other gastrocnemius and quadriceps, but the hamstrings only exert joint positions. The subjects used in both studies differed an antagonistic moment at the knee when the net moment at significantly in stature and mass from those used to obtain the hip is flexor. In other cases, the role of the hamstrings is PCSAs and moment arms. Consequently, moment arms were removed from equation 2. scaled to the subjects on the basis of height. Brand et al. (1986) have found that it is inaccurate to scale PCSAs on the basis of Literature study: calculation of muscle stresses height or mass alone, but they do not examine the accuracy of Calculation of muscle stresses from moments of force scaling for both together. Scaling PCSAs on the basis of presented in the literature were made for studies by Alexander mass/height allows comparison between short stocky and tall and Vernon (1975) and Bobbert and van Ingen Schenau (1988) thin people, although it does not take into account the degree using equations 1–3. Alexander and Vernon (1975) provided of body fat. diagrams of the position of the in contact with the ground at the point of peak ankle and knee moments of force during walking, running, jumping and landing from a jump. These Results were used to measure joint angles. Unfortunately, these authors Experimental study: running do not provide hip moments of force. In order to calculate the The subjects ran at speeds of 2.8–5.5 m s−1. Peak vertical moment exerted by the hamstrings at the knee when the knee ground reaction forces (averaging 2.9 times body weight at Human leg muscle stresses 67

4ms−1) were similar to previously reported forces (Cavanagh in the gastrocnemius and the hamstrings. However, in this and Lafortune, 1980; Dickinson et al. 1985; Munro et al. 1987; experiment, no differences in timing were observed. Miller, 1990). The maximum braking forces exerted during running at 5 m s−1 were rather high as the subject decelerated Literature study over the platform owing to the proximity of the wall of the Stresses calculated from Alexander and Vernon’s (1975) laboratory. This has resulted in peak moments and muscle peak moments of force may not represent the point in the stride stresses for the ankle for running at 5 m s−1 which are smaller at which peak stresses occur; however, they should be than those for running at 4 m s−1 (see Table 5) (three of the relatively close. Peak knee stresses taken from Bobbert and van sequences for running at 4 m s−1 did exhibit deceleration, but Ingen Schenau (1988) did not correspond with peak knee peak moments of force and muscle stresses did not occur moment of force because of the large moment exerted at the during this part of the stride). During running at 4 m s−1, the knee by the hamstrings when the knee is very bent at the start standard deviations for all joints are rather large owing to of the push-off phase, which is when peak stresses occurred. subject variability and because one subject was a rearfoot and Peak hip and peak ankle stresses did correspond with peak the other a forefoot striker (for individual data, see Thorpe, moments of force at these joints. Table 6 presents these results. 1997). This does not affect running at other speeds because both the sequences for running at 3 m s−1 are from the forefoot striker and those for running at 5 m s−1 are from the rearfoot Discussion striker. Peak moments at the hip occurred slightly before peak Table 2 compares PCSA values from cadavers and from knee moments and peak ankle moments slightly after peak MRI and CT analyses of healthy living subjects. The MRI knee moments. measurements are, in many cases, three times as large as those reported by Alexander and Vernon (1975) and Wickiewicz et Experimental study: jumping al. (1983). In general, cadavers which become available are All jumping records were of countermovement jumps with older individuals who may have been ill for some time and in both feet on the force plate; the recorded force was halved to whom muscle atrophy and myopathies are more likely to have obtain the force on one foot. Forces are similar to those been present before death. In addition, muscle properties are previously reported (Alexander and Vernon, 1975; Bobbert subject to morphological changes as a result of fixation and van Ingen Schenau, 1988; Pandy and Zajac, 1991). Peak treatment. Consequently, the use of cadaveric data greatly moments and muscle stresses are shown in Table 5. Peak overestimates the stresses exerted by muscle groups. quadriceps moment does not necessarily occur at the same time Physiological experiments on isolated mammalian muscles as peak knee moment, because it depends in part on the forces give values for maximum isometric stress between 100 and

Table 5. Mean values for peak moments and stresses at the hip, knee and ankle in running and jumping Running High Long 3ms−1 4ms−1 5ms−1 jump jump Number of trials analysed (N)26353 Peak ankle moment (N m) 195±30 230±42 181±7 151±26 157±21 Force in triceps surae (kN) 4.1±0.6 4.9±1.0 3.7±0.2 3.3±0.6 3.5±0.5 Stress in triceps surae (kN m−2) 127±20 151±30 114±6 101±18 107±14 Peak knee moment (N m) 238±2 278±110 326±53 213±38 76±8 Gastrocnemius moment at knee (N m) 16±0 19±5 13±4 33±6 34±3 Hamstring moment at knee (N m) 0 4±5 0 16±15 50±8 Peak quadriceps moment (N m) 254±3 299±108 339±51 262±29 160±12 Force in quadriceps (kN) 5.6±0.1 7.1±2.5 7.7±1.5 7.8±0.3 5.4±0.6 Stress in quadriceps (kN m−2) 199±5 255±89 275±55 277±10 191±21 Peak hip moment (N m) 103±1 31±215 235±68 193±25 251±30 Rectus moment at hip (N m) 39±7 37±37 51±16 6±3 2±1 Peak hip extensor moment (N m) 142±6 63±255 286±84 198±27 253±31 Force in hip extensors (kN) 2.4±0.1 3.6±1.2 4.8±1.0 3.9±1.1 6.1±1.9 Stress in hip extensors (kN m−2) 74±2 110±37 146±32 120±34 187±60

Extensor and plantar flexor moments are shown as positive and flexor moments as negative (no negative values shown). Values are means ± S.D. Hip moment is the net moment required of the hip muscles. Hamstrings moment is the calculated moment required of the hamstrings, adductors and gluteus maximus after taking account of the moment exerted by the rectus femoris. Knee moment is the net moment required of the knee muscles. Quadriceps moment is the calculated moment required of the quadriceps muscles, after taking account of the moments exerted by the gastrocnemius and the hamstrings. The hamstrings are only active at the knee when the net moment at the hip is flexor. 68 S. K. S. THORPE AND OTHERS

Table 6. Stresses at the hip, knee and ankle calculated from moments of force presented in Alexander and Vernon (1975) and Bobbert and van Ingen Schenau (1988)* Run Long Landing from High Walk 1 Walk 2 3.5–4 m s−1 jump a jump jump* Ankle moment (N m) −20 96 220 103 100 138 Force in triceps surae (kN) 0.4 2.3 5.2 2.5 2.4 2.5 Stress in triceps surae (kN m−2) 14 72 166 78 75 73 Knee moment (N m) 97 13 192 112 142 155 Gastrocnemius moment at knee (N m) −21227131214 Hamstring moment at knee (N m) 42 48 23 73 34 66 Quadriceps moment (N m) 137 73 241 198 189 235 Force in quadriceps (kN) 3.4 2.2 6.4 8.1 7.8 7.7 Stress in quadriceps (kN m−2) 127 85 241 307 292 289 Hip moment (N m) 136 115 44 187 111 185 Rectus moment at hip (N m) 19 24 37 22 42 27 Hip extensor moment (N m) 155 139 81 209 153 212 Force in hip extensors (kN) 2.4 2.8 1.3 5.2 2.3 4.0 Stress in hip extensors (kN m−2) 82 98 44 181 79 138

For jumping, the moment of force has been halved to estimate the value for one leg. Walk 1 and walk 2 correspond, respectively, to the points at which the knee moment and ankle moment are highest. In running, long jump and landing from a jump, maximum moments at the knee and ankle occurred simultaneously (Alexander and Vernon, 1975). Thus, the ankle moment in walk 1, the knee moment in walk 2 and all the hip moments for Alexander and Vernon’s (1975) data are not peak values. However, the moments of force and muscle stresses for the high jump (Bobbert and van Ingen Schenau, 1988) are peak values. Extensor and plantar flexor moments are shown as positive and flexor moments as negative. Cutts (1988) does not provide physiological cross-sectional areas (PCSA) for the individual heads of the biceps, which are needed to calculate the moment of the long head at the hip. Friederich and Brand (1990) and Alexander and Vernon (1975) both found that the long head of the biceps was approximately 80 % of the total biceps PCSA and consequently it has been assumed that this is the case for the data taken from Cutts (1988). Terminology applies as for Table 5.

300 kN m−2 (Wells, 1965; James et al. 1995; for a review, see our experimental study. The largest discrepancy is for quadriceps Josephson, 1993). Maximum muscle stresses during stress in the long jump, for which Table 6 shows a substantially lengthening may be as much as 75 % greater than this value higher value than Table 5. Alexander and Vernon (1975) (Katz, 1939; Cavagna and Citterio, 1974; Flitney and Hirst, calculated stresses from the same moments of force as the 1978). In vivo measurements of muscle force production have recalculated values, but using cadaveric data to obtain muscle provided maximum isometric stresses of 105 kN m−2 for the physiological cross-sectional area. They obtained muscle stresses triceps surae (Fukunaga et al. 1996) and 250 kN m−2 for the of 420 kN m−2 in the triceps surae and 360 kN m−2 in the quadriceps (Narici et al. 1992). The peak stresses shown for quadriceps for running at 3.5–4 m s−1, and 210 kN m−2 in the the triceps surae in Table 5 range from 101±18 kN m−2 (mean triceps surae and 380 kN m−2 in the quadriceps for standing high − ± S.D.) in a standing high jump to 151±30 kN m 2 in running jumps. These values are substantially higher than those obtained at 4 m s−1. Peak quadriceps stresses in Table 5 range from in the present study because the cadaveric PCSAs are much 191±21 kN m−2 in a standing long jump to 277±10 kN m−2 in smaller than those obtained from MRI and consequently result in a standing high jump. The peak stresses in the triceps surae higher muscle stresses. for running at 4 m s−1 and in the quadriceps for a standing high The peak stresses exerted in the triceps surae are lower than jump are higher than the in vivo maximum isometric stresses those for the quadriceps in all activities, as would be expected for these muscle groups (Fukunaga et al. 1996; Narici et al. from the in vivo measurements of maximum isometric stress, 1992). The results for running at 4 m s−1 may suggest that the which show that the value for the triceps surae is less than half triceps surae are acting eccentrically when peak stresses occur that for the quadriceps (Fukunaga et al. 1996; Narici et al. because, although the ankle is plantarflexing (shortening the 1992). Whilst physiological experiments on isolated muscle muscle), the knee is extending (lengthening the preparations have suggested that the force-generating potential gastrocnemius). However, the peak stresses for standing high of individual muscle fibres is relatively constant, there is an jumps occurred as the subject began to push off from a increasing body of evidence to suggest that the mechanisms by crouched position, at which time the quadriceps were which sarcomere force is transmitted through the muscle shortening. matrix to the tendon may result in different muscle stresses for In general, the stresses calculated from moments of force different muscles (Fukunaga et al. 1996). This may be related presented in the literature are in good agreement with those in to a number of factors such as the role of the muscle interfibre Human leg muscle stresses 69 matrix in force generation (see Trotter, 1993) and the tendency lower limb and to stabilise the upper body. He suggests that it of some fibres to taper over half their length (Eldred et al. may be fine adjustments of the trunk that increase the 1993). Some apparent differences between muscles isometric variability, thus disguising major patterns which may stress may also be an artefact of ambiguous definition of otherwise be evident. PCSA. The cross-sectional areas of muscles must change as In conclusion, the present study has shown that using MRI they lengthen and shorten, if their volumes remain constant. measurements of physiological cross-sectional areas of For example, Narici et al. (1996) found that the PCSA of the muscles of healthy living subjects enables calculations to be gastrocnemius medialis increases by 51 % as the ankle angle made of muscle stresses exerted during various human increases from 90 to 150 °. The stress corresponding to a given activities. The stress values obtained are lower than those muscle force will depend on the joint angle at which the PCSA calculated using PCSAs of cadaveric material, but are is measured. However, this seems unlikely to explain the consistent with those obtained using isolated muscle differences in PCSAs seen in Table 2, since Fukunaga et al. preparations and in vivo isometric measurements. (1992) determined the PCSAs with the ankle at approximately 120 ° and the knee extended. In this position, if the triceps surae We are grateful to the subjects who took part in this study and quadriceps were taut, the fibres of both would have been and to two anonymous reviewers. at the short end of their working ranges of lengths. Narici et al. (1992) do not provide joint angles but say that the leg was References fully extended, and this seems a likely position for all studies ALEXANDER, R. MCN. (1983). Animal Mechanics, 2nd edn. Oxford: carried out on cadaveric material. Blackwell. Mean peak joint moments for running are 210±39 N m ALEXANDER, R. MCN. AND VERNON, A. (1975). The dimensions of the (mean ± S.D.) at the ankle, 284±87 N m at the knee and knee and ankle muscles and the forces they exert. J. Human Movmt 100±180 N m at the hip; those for jumping are 153±23 N m, Stud. 1, 115–123. 162±77 N m and 215±39 N m, respectively. These results BENEKE, R., NEUERBURG, J. AND BOHNDORF, K. (1991). Muscle cross compare well with those in the literature (see Table 7). section measurement by magnetic resonance imaging. Eur. J. appl. Tables 5 and Table 7 both indicate that there is great variability Physiol. 63, 424–429. in peak hip moments during running. This agrees with results BOBBERT, M. F. AND VAN INGEN SCHENAU, G. J. (1988). Co-ordination obtained by Winter (1983) and Mann (1981) and those in vertical jumping. J. Biomech. 21, 249–262. reviewed in Winter (1980). Winter (1983) relates this BRAND, R. A., PEDERSEN, D. R. AND FRIEDERICH, J. A. (1986). The sensitivity of muscle force predictions to changes in physiologic variability to the dual role of the hip flexors and extensors cross-sectional area. J. Biomech. 19, 589–596. during running, in that they are required both to support the CAVAGNA, G. A. AND CITTERIO, G. (1974). Effect of on the elastic characteristics and the contractile component of frog striated muscle. J. Physiol., Lond. 239, 1–14. Table 7. Mean peak net joint moments of force exerted in CAVANAGH, P. R. AND LAFORTUNE, M. A. (1980). Ground reaction various activities forces in distance running. J. Biomech. 13, 397–406.

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